Chapter 8 Infinitive series
8.1 The concepts and characters of infinite series
8.1.1 The concepts of constant term progression
8.1.2 The convergence and divergence of infinite series
8.1.3 The characters of convergent series
Exercises
8.2 Positive series and its convergence test
8.2.1 The basic characters of positive series
8.2.2 The comparison test of positive series
8.2.3 d'Alembert method of positive series
8.2.4 The root test of positive series
Exercises
8.3 Arbitrary term progression
8.3.1 Alternating series and Leibniz Principle
8.3.2 The absolute value method of arbitrary term progression
Exercises
8.4 Power series
8.4.1 Function series
8.4.2 Power series and its convergent interval
8.4.3 The properties of power series
Exercises
8.5 Unfold functions into power series
8.5.1 Taylor series
8.5.2 The method to unfold functions into power series
Exercises
Summary
Quiz
Exercises
Chapter 9 Differential equations
9.1 Basic concepts of differential equation
Exercises
9.2 First-order differential equation
9.2.1 Separable differential equation
9.2.2 Homogeneous differential equation
9.2.3 First-order linear differential equation
9.2.4 Bernoulli equation
Exercises
9.3 Reducible high-order differential equation
9.3.1 The formy("~=f(x)
9.3.2 The form y"= f(x,y')
9.3.3 The formy"=f(y,y')
Exercises
9.4 High-order linear differential equation
9.4.1 The property and structure of solution of second-order linear differential
equation
9.4.2 The property and structure of solution of high-order linear differential
equation
Exercises
9.5 Second-order linear differential equation with constant coefficients
9.5.1 Second-order homogeneous linear differential equation with constant
coefficients
9.5.2 Second-order inhomogeneous linear differential equation with constant
coefficients
9.5.3 Vibration equation
Exercises
Summary
Quiz
Exercises
Chapter 10 Vectors and analytic geometry of space
10.1 Space right angle coordinate system
10.1.1 The space right angle coordinate system
10.1.2 Right angle coordinate of spatial point
10.1.3 Distance between two points in space
Exercises
10.2 Vector algebra
10.2.1 Concepts of vector
10.2.2 Linear operations of vector
10.2.3 Coordinates of vector
10.2.4 Dot product of two vectors
10.2.5 Vector product of two vectors
Exercises
10.3 Plane or space straight line
10.3.1 Plane and its equation
10.3.2 Included angle between two planes
10.3.3 Distance from point to plane
10.3.4 Space line and its equation
10.3.5 Included angle between two straight lines
10.3.6 Angle between straight line and plane
Exercises
10.4 Curved surface and space curve
10.4.1 Equation of spatial curved surface
10.4.2 Equation of spatial curve
10.4.3 Quadric surface
Exercises
Summary
Quiz
Exercises
Chapter 11 Differentiation of multivariable function and its application
11.1 The concept of multivariable function
11.1.1 Plane point set and n-dimensional space
11.1.2 Multivariable function
11.1.3 The limit of multivariable function
11.1.4 Continuity of multivariable function
Exercises
11.2 Differential method of multivariate function
11.2.1 Partial derivative
11.2.2 Perfect differential and its applications
11.2.3 Differential method of multivariable compound function
11.2.4 Derivative of implicit function
Exercises
11.3 Direction derivative and gradient
11.3.1 Direction derivative
11.3.2 Gradient
Exercises
11.4 Geometric applications of the differential of muitivariable function
11.4.1 Tangent line and normal plane of space curve
11.4.2 Tangent plane and normal line of curve surface
Exercises
11.5 The extreme value of the multivariable function and the maximum and minimum
11.5.1 The extreme value of the multivariable function
11.5.2 The maximum and minimum of multivariable function
11.5.3 Conditional extremum Lagrange multiplier
Exercises
11 6 Taylor's formula of binary function
11.6.1 Taylor's formula of binary function
11.6.2 The proof of sufficient condition of extreme of binary function
Exercises
Summary
Quiz
Exercises
Chapter 12 Multiple integral
12.1 The concept and properties of double integrals
12.1.1 Examples
12.1.2 The definition of double integrals
12.1.3 The property of double integrals
Exercises
12.2 Calculation of double integrals
12.2.1 Calculate double integrals in rectangular coordinate system
12.2.2 Calculate double integral in the polar coordinate system
12.2.3 Application in the economic management
12.2.4 Variable substitution
Exercises
12.3 Triple integral and its calculation
12.3.1 The definition and property of triple integral
12.3.2 Evaluate the triple integral by space right angle coordinate
12.3.3 Calculate the triple integral by cylindrical coordinate
12.3.4 Calculate the triple integral by spherical coordinate
Exercises
12.4 Application of multiple integral
12.4.1 Applications in geometry
12.4.2 Applications in physics
Exercises
12.5 Integral with parameters
Exercises
Summary
Quiz
Exercises
Answers

本书为全英文教材，主要内容形成以函数、极限、连续、导数、积分、级数、微分方程等为明线，以简单经济函数模型、复利和连续复利、边际、弹性、经济优化模型等为暗线的课程体系，突出微积分的基本方法的理论学习及经济应用。